Tone Measurements Express VI

[Tpnini]

Hi!

I have a question about  the express VI - Tone Measurement Express VI (Sound and Vibration Toolkit)

I used this function to find the main peak of the FFT signal,

I would like to understand what is the deviation for these results,

I guess it depends on the resolution of the FFT signal

and the resolution is derived from the sample rate divided by the number of samples to read.

for example, if I have a rate of 12,000 sample/s and I read 4000 sample, the resolution is - 3Hz,

does it mean that the Tone Measurement VI will find peaks with a deviation of 3Hz?? (like - 150Hz, 153Hz, 156Hz...)

is anyone knows how does this Express VI works? 

[Bob_Schor]

I'm not quite sure what you mean by "deviation", but let me see if I can answer your question and explain the answer by asking a related question -- what is the lowest frequency you can resolve with an FFT, supposing you sample for a total time T?  Well, it would correspond to a frequency that had only one "wave" in time T.  In your example, T = 4000 samples/(12000 samples/second), so 1/T = 3 (1/s) = 3 Hz.  This also corresponds to the intervals between frequencies represented by the 2000 independent Amplitude/Phase results returned by the FFT.

Question -- why are there only 2000 Amplitude/Phase results?  If the frequency interval is 3 Hz, why is the highest frequency in the Spectrum "only" 3 Hz * 2000 = 6 kHz, particularly when you sampled at 12 kHz?  [Hint -- who was Nyquist?]

Bob Schor

[J_Webster]

First, I think you want to use the term "resolution" instead of "deviation". 

Second, it appears that the Tone Measurement routine doesn't simply return the frequency of the peak in the FFT.  Digging down into the vi and its sub-vis, it seems that it takes the peak bin and the bins on its right and left, and tries to estimate what the exact peak frequency and amplitude are...

I don't have time to go through and figure out exactly what's going on, but I suspect there is a paper somewhere that describes exactly what calculation they use. It doesn't look terribly complicated though.